# Solution toFET Circuit Problem Let’s break down the steps for solving the given problem: --- ## **Given Data** - \( K_{p}' = 100~\mu\text{A}/V^2 \) (for PMOS, \( M_P \)) - \( K_{n}' = 40~\mu\text{A}/V^2 \) (for NMOS, \( M_N \)) - \( V_{TN} = .6~V \) (NMOS threshold) - \( V_{TP} = -.6~V \) (PMOS threshold) - \( V_{DD} = 3.3~V \) - \( V_O = 1.65~V \) (desired output) --- ## (a) **What bias voltage is required at \( V_{I} \) to set \( V_{O} = 1.65~V \)?** ### **Step 1: Node Voltages** - Source of \( M_P \): \( V_{DD} = 3.3~V \) - Source of \( M_N \): Ground = \( ~V \) - Drain of both (node \( V_O \)): \( 1.65~V \) ### **Step 2: Gate-Source Voltages** Let \( V_G \) be the gate voltage for both transistors (since both gates are tied together). - For \( M_P \) (PMOS, top transistor): - Source: \( 3.3~V \) - Gate: \( V_I \) - \( V_{SGP} = V_{S} - V_{G} = 3.3 - V_I \) - For \( M_N \) (NMOS, bottom transistor): - Source: \( ~V \) - Gate: \( V_I \) - \( V_{GSN} = V_I - = V_I \) --- ### **Step 3: Currents (In Saturation)** For both, the currents must be equal: \( I_{DP} = I_{DN} \). #### **NMOS:** \[ I_{DN} = K_n (V_{GSN} - V_{TN})^2 = 40~\mu\text{A}/V^2 \cdot (V_I - .6)^2 \] #### **PMOS:** \[ I_{DP} = K_p (V_{SGP} - |V_{TP}|)^2 = 100~\mu\text{A}/V^2 \cdot (3.3 - V_I - .6)^2 \] Set equal: \[ 100 (2.7 - V_I)^2 = 40 (V_I - .6)^2 \] --- ### **Step 4: Solve for \( V_I \)** \[ \frac{100}{40} (2.7 - V_I)^2 = (V_I - .6)^2 \] \[ 2.5 (2.7 - V_I) = V_I - .6 \] \[ 2.5 \cdot 2.7 - 2.5 V_I = V_I - .6 \] \[ 6.75 - 2.5 V_I = V_I - .6 \] \[ 6.75 + .6 = V_I + 2.5 V_I \] \[ 7.35 = 3.5 V_I \] \[ V_I = \frac{7.35}{3.5} \approx 2.10~V \] --- ## (b) **What are the drain currents of \( M_P \) and \( M_N \)?** Plug \( V_I = 2.10~V \) into either current equation: \[ I_D = 40~\mu\text{A}/V^2 \cdot (2.10 - .6)^2 = 40~\mu\text{A}/V^2 \cdot (1.5)^2 = 40 \cdot 2.25 = 90~\mu\text{A} \] --- ## **Final Answers** ### **(a) Bias voltage at \( V_I \):** \[ \boxed{2.10~V} \] ### **(b) Drain currents of \( M_P \) and \( M_N \):** \[ \boxed{90~\mu\text{A}} \] --- **Summary Table:** | Parameter | Value | |---|---| | \( V_I \) | 2.10 V | | \( I_{DP} = I_{DN} \) | 90 μA | --- **Figure 2 MOSFET Circuit** *The calculations above apply to the circuit shown in the image.*